"Local" exponential transform methods for the Monte Carlo simulation of multigroup transport problems.

Abstract

Variance reduction methods are essential for reducing the running times of many Monte Carlo transport calculations. To optimize the efficiency of these techniques, substantial effort is often spent by the code user, who must choose one or more "biasing" parameters. Unfortunately, the optimal values of these parameters depend on the problem to be solved; a good choice depends on experience and luck or a lengthy process of trial-and-error. In an effort to develop efficient Monte Carlo variance reduction methods in which the computer itself automatically determines the biasing parameters, we present in this thesis a new "local" exponential transform method for multigroup general-geometry transport problems. The Local Exponential Transform method is an approximation to a zero variance method, and is derived by the following three steps: (1) A zero-variance method is formulated, in which all source particles are guaranteed to score with exactly the same (correct) weight. This method is impractical because it requires knowledge of the exact solution of an adjoint transport problem. (2) A diffusion approximation to the adjoint transport problem is formulated and solved numerically. (3) Within each spatial cell, the spatial variation of the adjoint transport flux is approximated by an exponential function whose amplitude and decay constants (the biasing parameters) are determined by the numerical diffusion solution and the elementary solution to the transport equation in one group homogeneous slab geometry. In this way, the zero-variance method is approximated and made practical. We have implemented the new Local Exponential Transform method in a one dimensional code and in the general-geometry multigroup Monte Carlo code ANDY. Numerical comparisons show that the Local Exponential Transform method is very efficient for multigroup isotropic and linearly anisotropic scattering general-geometry transport problems and usually has a significantly better figure of merit than conventional Splitting with Russian Roulette. This is especially true for problems in which the spatial behavior of the solution is locally exponential. However, more work needs to be done for problems with voided or highly scattering regions. In such problems, the flux does not behave in a locally exponential manner, and the Local Exponential Transform method can become less effective.